Astate administered standardized reading exam is given to eighth grade students. the scores on this exam for all students statewide have a normal distribution with a mean of 507 and a standard deviation of 39. a local junior high principal has decided to give an award to any student who scores in the top 10% of statewide scores. how high should a student score be to win this award? give your answer to the nearest integer. for on how to input a numeric answer, see the instructions for entering numeric response.

The minimum score to be obtained to place in the top 10% and win this award is, 557

Step-by-step explanation:

Since the score obtained by eighth grade students is a normal random variable with a mean and and we are interested in the minimum score required for a student to be in the top 10% of all scores, It is necessary to calculate the 90th percentile for the cumulative probability distribution of the score variable in the reading test.

The variable is a standard normal variable and therefore, is the score corresponding to the standardized value z.

We must calculate the value of k such that , then, using the inverse standard normal distribution you have to y hence

Conclusion: The minimum score to be obtained to place in the top 10% is 557

step-by-step explanation:

first, eliminate the parenthesis:

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2

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second, group like terms:

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third, combine like terms:

(

3

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→

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1

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8

step-by-step explanation: